A teaching-learning-based optimization algorithm for the environmental prize-collecting vehicle routing problem

The present research proposes a new Vehicle Routing Problem (VRP) variant, the Environmental Prize-Collecting Vehicle Routing Problem (E-PCVRP). According to the original PCVRP formulation, the scope of the problem is to maximize the total collected prize from the visited nodes and simultaneously minimize the fixed vehicle-utilization cost and the variable cost. In the E-PCVRP formulation, the variable cost is not solely expressed as a vehicle-covered distance but as a load-distance function for CO2 emissions minimization. The Teaching-Learning-Based Optimization (TLBO) algorithm is selected as the solution approach. However, TLBO is designed to address continuous optimization problems, while the solution of the E-PCVRP requires a discrete-numbered representation. Thus, a heuristic encoding/decoding technique is proposed to map the solution in a continuous domain, i.e., the Cartesian space, and transform it back to the original form after applying the learning mechanisms, utilizing the Euclidean Distance. The encoding/decoding process is denoted as CRE, and it has been incorporated into the standard TLBO algorithmic scheme, and as such, the proposed TLBO-CRE algorithmic solution approach emerges. The effectiveness of the TLBO-CRE is demonstrated over computational experiments and statistical analysis in comparison to the performance of other bio-inspired algorithms and a mathematical solver.